Lawes, who is capable of playing as both a lock and in the back row, damaged his pectoral muscle in training during the week and will now miss Sunday's (AEDT) match against Wales in Cardiff.
Capped 87 times by England, Lawes has also been ruled out of next month's Six Nations fixtures against France and Ireland.
"Unfortunately, Courtney picked up a knock and that means he won't be available for us for the rest of the Six Nations," England attack coach Simon Amor revealed.
"We are still waiting for a bit more of that detail but it was just a bit of a fall and he tweaked his pec there," Amor added. "It's very disappointing, but these things happen."
Lawes's place in the back row has been taken by Mark Wilson with Amor insisting England will cope with the loss of the 32-year-old Northampton stalwart.
"He (Lawes) brings a lineout threat and a great defensive energy," Amor said.
"Of course that's a strength but we have some really fantastic players, particularly Mark Wilson, who can get around the field and provide that energy, particularly around the breakdown."
Lawes is the latest England back-row forward to be sidelined, with Jack Willis out for the season with a knee injury suffered against Italy while Sam Underhill has yet to feature in this year's Six Nations because of a hip problem.
England goes into the Wales match on the back of a 41-18 win over Italy.
But defeat in Cardiff would all but end England's hopes of a successful title defence after a shock opening loss to Scotland, while a win for Wales would see it claim the Triple Crown and stay on course for a Grand Slam.
"It is make or break, that's where it sits," Amor said.
"Certainly the two (England-Wales) games I've been involved with the team, it's been a one-score game, so we know it's going to be close, tight, with those really critical moments.
"We've been working really hard on our game this week to make sure we are on the right side of those critical moments."